UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A)

Transcription

1 UC Berkeley Haas School of Business Economic Analysis for Business Decisions (EWMBA 201A) Production and the costs production (PR ) Cost concepts and the relations among costs Lectures 3-4 Aug. 20, 2011

2 Production (PR 6.1) In the production process, firms turn inputs (labor, capital, materials) into output. The theory of the firm explains how a firm makes (optimal) production decisions and how its costs vary with its output. Like the theory of the consumer, the theory of the firmcanbeusedto predict, postdict (explain), and prescribe.

3 The production function The production function indicates the (highest) output that the firm can produce for a given combination of inputs. For our purposes it is convenient to consider only the case of two inputs capital and labor. We can the write the production function as = ( ) The Cobb-Douglas production function is widely used to represent the technology of production = where 0.

4 Returns to scale (PR 6.4) Returns to scale is the rate is the rate at which output increases as inputs, and, are increased proportional. Increasing output more than doubles when inputs are doubled. Decreasing output less than doubles when inputs are doubled. Constant output doubles when inputs are doubled. Returns to scale vary considerably across and within industries. Other things being equal, the greater the return to scale in an industry, the larger the firms are likely to be (a natural monopoly!).

5 The Cobb-Douglas production function exhibits increasing, constant, or decreasing returns to scale if respectively = Note: and also determines marginal product of capital and labor. The law of diminishing marginal returns 0 holds for most production processes.

6 The short run vs. the long run (PR 6.1) The short run is the period of time in which the quantities of one or more inputs cannot be changed. The long run is the period of time in which the quantities of all inputs cannot be changed. Typically, we assume that in the sort run labor is variable and capital is fixed (more later!). John Keynes: The long run is a misleading guide to current affairs. In the long run we are all dead...

7 Costs (PR 7.1) Question: What is the cost of an activity (producing a good or service)? The obvious answer might seem the money spent on that activity. Like so many obvious answers, this is not (necessarily) the correct answer. Thecorrectwaytoconsiderthecosttobethevalueofthemosthighly valued forgone activity the value of the best alternative decision). Note: Economists describe this way of viewing cost as considering the opportunity cost of an activity or decision.

8 Accounting cost Actual expenses plus depreciation charges to capital (this naive view, focusing on expenditures can lead one to make bad decisions). Economic cost Cost of utilizing inputs in production, including opportunity cost (for example, the imputed value of the forgone rent on owned office space). Note: A sunk expenditure (cannot be recovered or avoided over the relevant decision-making horizon is not an economic cost).

9 Cost concepts Fixed cost ( ) does not vary with the level of production and can be eliminated only by shutting down (not sunk cost). Variable cost ( ) varies as output varies. Total cost ( or ) isthetotaleconomiccost of production ( ) = + ( ) Marginal cost /( ) is the increase in cost resulting from the production of one extra unit of output = =

10 Relations among costs in the short run (PR 7.2) We next explore the relations among total cost, average cost, and marginal cost from an algebraic and graphical perspectives. Recall from the previous section that ( ) = ( ) ( 1) and observe that we can express variable cost as follows ( ) = (1) + (2) + + ( ) = P =1 ( ) The variable total of producing units is the sum of the marginal costs of producing the first units.

11 The average variable cost ( ) of producing units is P =1 ( ) ( ) = ( ) = and the average total cost ( ) of producing units is ( ) = ( ) = ( ) +

12 Result ( ) If average variable cost ( ) is decreasing, then marginal cost ( ) is less than average variable cost. ( ) If average variable cost is increasing, then marginal cost is greater than average average variable cost. Anotherwaytostatethisconclusionis ( +1) ( ) then ( +1) ( ) ( +1) ( ) then ( +1) ( ) PR Figure 7.1 here

13 Proof Case ( ): ( +1) = ( +1)+P =1 ( ) +1 If ( +1) ( ), then = ( +1) +1 + ( ) +1 ( +1) ( +1) = +1 Case ( ) is established similarly ( ) ( ) = ( ) +1

14 Costs in the short run and the long run (PR 7.9) The relationship between short-run and long-run cost can be fairly complicated. In the long run, the firm can change the quantity of any of its input, whereas in the short run the quantity of at least one input is fixed. As a result, the long-run average cost curve never lies above any of the short-run average cost curves (an envelope). PR Figure 7.9 here

15 PR 7 exercises 1-5. Problem set II